Law of substitution Law of substitution

# Law of substitution

## Law of substitution (2nd law of Gossen)

The law of substitution is also known as the law of Equi-marginal utility or the law of maximum satisfaction or the law of indifference or the proportionate rule. This law was first developed by H. H Gossen. Therefore, this law is also known as the second law of Gossen. Professor Marshall has developed and given the present shape of this law.

This law states that” In order to get maximum satisfaction a consumer should spend his limited income on different commodities in such a way that the last rupee spent on each commodity yields him equal marginal utility.

Algebraically,

Where,
MUx = marginal utility of x commodity
MUy = marginal utility of y commodity
Px = price of x commodity
Py= price of y commodity

This law is equally applicable in case of more than 2 commodities which can be expressed as
The law of substitution is also known as’ the law of maximum satisfaction because the consumer can maximize his/her satisfaction by spending in accordance with this law. It is also called the ‘law of substitution’ because the consumer will go on substituting one commodity with higher marginal utility or another commodity with lower marginal utility until the marginal utility of each commodity is equal.

#### Assumptions of Law of substitution:

1. The consumer should be rational.
2. Utilities are measured in cardinal numbers.
3. Applicability of diminishing marginal utility.
4. Constant marginal utility of money
It can be explained by the help of the following schedule:
 Units of money MU of Tea MU of coffee 1 10 12 2 8 10 3 6 8 4 4 6 5 2 3

A rational consumer would like to get maximum satisfaction from Rs.5. A sensible consumer will spend Rs.2 on tea and Rs.3 on coffee and will get maximum equal satisfaction. It can be further explained by the help of the following diagram:
In the above figure, MU1 is the marginal utility curve for tea and MU2 is the marginal utility curve for coffee. When a consumer spends Rs.1 on tea and Rs.2 on the coffee he will get maximum equal satisfaction but the total amount spend I.e. Rs (1+2) = Rs.3 will be less than his budget. When a consumer spends Rs.3 on tea and Rs.4 on the coffee he will get maximum equal satisfaction but the total amount spent will be more than his budget. So, he will spend Rs.2 on tea and Rs.3 on the coffee he will get maximum equal satisfaction and he can spend the total budget to derive it.

### Limitations or exceptions of Law of substitution

1. If the consumer is ignorant or blindly follows customs or fashion, he will make the wrong use of money.
2. This law is based on the assumption that commodities are substitutable. This is an unrealistic assumption. Every commodity cannot be substituted.
3. The principle of maximum satisfaction is based on the unrealistic assumption of cardinal measurement of utility.
4. Marginal utility of money never remains constant.
5. This law has no place when the resources are unlimited as in the case of the free gifts of nature.
6. The alternatives that a consumer chooses may be uncertain and even risky.

### Importance/significance of the law of substitution.

1. Basis of consumption
The consumer is assumed to be rational. The law of substitution helps every consumer to maximize his/her utility by equalizing the marginal utilities obtained from different commodities.
1. Important in the field of production
The producer has to use several factors of production in order to maximize net profit. For this purpose, he will substitute one factor for another till their marginal productivity is made the same.
1. Important in the field of exchange
In the exchange, this law applies because the exchange is the principle of substitution itself. When we sell a commodity, we get money. With this money, we buy another commodity. Therefore we have really substituted commodity for money.
1. Important in distribution
In distribution, we are concerned with the determination of rewards of various factors of production I.e. determination of rent, wages, interest, and profit. That means we are substituting factors of production for rewards.
1. Important in public finance
The law of substitution also applies to public finance. The government must try to maximize the welfare of the community. For this, the government must take down all the wasteful expenditures and divert on the productive sector.
1. Price determination
When a commodity becomes scarce and its price becomes high, in order to bring its price down we start substituting an abundant commodity for it.